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Abstract

We report the experimental demonstration of the superluminal propagation of multi-spatial-mode images via four-wave mixing in hot atomic vapor, in which all spatial sub-regions propagate with negative group velocities. We investigate the spatial mode properties and temporal reshaping of the fast light images, and show large relative pulse peak advancements of up to 64 % of the input pulse width. The degree of temporal reshaping is quantified and increases as the relative pulse peak advancement increases. When optimized for image quality or pulse advancement, negative group velocities of up to
vg=−c880 and
vg=−c2180, respectively, are demonstrated when integrating temporally over the entire image. The present results are applicable to temporal cloaking devices that require strong manipulation of the dispersion relation, where one can envision temporally cloaking various spatial regions of an image for different durations. Additionally, the modes involved in a four-wave mixing process similar to the present experiment have been shown to exhibit quantum correlations and entanglement. The results presented here provide insight into how to tailor experimental tests of the behavior of these quantum correlations and entanglement in the superluminal regime.

Figures (4)

Schematic showing (1a) the double-lambda level scheme, (1b) the typical probe gain lineshape with probe detuning indicated, and (1c) the experimental setup. The pump beam is detuned ≈ 400 MHz to the blue of the 85Rb D1 line, with the probe blue-detuned ≈ 3.0 GHz relative to the pump. The probe’s center frequency is set to be on the blue wing of the probe gain line. After the 4WM interaction, the probe pulses are imaged onto a gated, intensified CCD camera. The pulses are able to be time-resolved down to 2.44 ns temporal bins.

Negative group velocity of a carrier pulse resulting in an advanced pulse peak with a spatially multi-mode image, in this case the letter “c”. The green curve is the detected probe pulse, integrated over the image, when the pump is not present. The red curve is the detected superluminal amplified probe pulse, integrated over the image, when the pump is turned on. A relative advancement of ≈ 50 ns, corresponding to a group velocity of
vg=−c880, is shown. The probe pulse in this measurement was shaped with the letter c, and the arrival time was monitored with a gating width of 3 ns. The snapshots across the top of the graph show the cross section of the beam at equidistant times between 120 ns and 480 ns (top row: reference, lower row: superluminal pulse). The two insets show the full time-integrated images. The advanced image (left inset) shows distortion due to inhomogeneous gain, Kerr-lensing and leaked pump light, but the principal shape clearly persists. The superluminal pulse group velocity can be determined pixel-wise for the image, as well as integrated over the whole image. The peak gain of the unnormalized superluminal pulse is ≈ 2.1.

Gain (3a) and relative pulse peak advancement (3b) of the superluminal probe pulses for the input probe with a Gaussian spot. Each superpixel corresponds to a 12×12 binning of pixels on an intensified CCD camera. The pump beam is slightly elliptical, with a waist of ≈ 750μm×950μm. Relative pulse peak advancement is seen to increase from ≈ 40 ns to ≈ 100 ns from the right-hand side to the left-hand side of the probe spot. The gain also varies spatially, with the highest gain regions corresponding to the lowest relative pulse peak advancements. The ellipses correspond to the 1/e2 intensity of the detected amplified probe spots. Uncertainties in the relative pulse peak advancement are largest toward the edges of the image (≈ 10 ns), due to statistical uncertainties from a decreased signal-to-noise ratio resulting from the lower intensities. The uncertainty in the relative advancement near the inner region of the image is ≈ 3 ns, resulting from the minimum detector gating time.

Plot of the advanced pulse versus time when the system is optimized for maximum advancement rather than image quality. The red and green curves are the advanced pulse and reference pulse intensities integrated over the entire Gaussian spot. A pulse peak advancement of 124 ns is shown, corresponding to a relative pulse peak advancement of 64 % compared to the input pulse FWHM, and a group velocity of
vg=−c2180. The gain in this case is ≈ 5, and the relative degree of reshaping is D ≈ 0.8. Ringing on the trailing edge of the advanced pulse is seen, as expected for very large relative advancements.